We also expect to extend the results of this article to programs with resources
of arbitrary capacity, where we still have some control of the homotopy type of
the spaces generated by the semantics of such programs. This is, after all, part
of an endeavor to better understand the geometries that can appear in the study
of rewriting, concurrent and distributed systems, where other primitives
(test-and-set and all read-modify-write statements) will generate different
types of geometries. The relationship between metrics and (di-)homotopies,
unravelled in this paper, may also pave the way to considering timed concurrent
models, studied up to deformation (and amenable to state-space reduction
techniques [1]}). This has actually already been used in a different
context, in robotics, by Ghrist and collaborators, to design efficient
algorithms, see [2]}.
